There are some little mistakes you have like syntax of forloop is wrong and to clear root array use removeAll function. it should be like:-
projectModel.dateProject.removeAll();//clear root array
for(var i = 0;i<projectItems.length;i++){
projectModel.dateProject.push(projectItems[i]) //don't use '()' with projectModel.dateProject
}
Add data-binding for nested observable array in view.
<div id="projectShow">
<!-- ko foreach: dateProject -->
<span data-bind="text:createDay"></span>
<ul>
<!-- ko foreach: projectList -->
<li data-bind="text:checkResult"></li>
<li data-bind="text:labelArr"></li>
<!-- /ko -->
</ul>
<!-- /ko -->
</div>